課程名稱 |
數學建模 Mathematical Modeling |
開課學期 |
105-2 |
授課對象 |
理學院 應用數學科學研究所 |
授課教師 |
林太家 |
課號 |
MATH5426 |
課程識別碼 |
221 U6130 |
班次 |
|
學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期五7,8,9(14:20~17:20) |
上課地點 |
天數101 |
備註 |
與洪子倫、鄧君豪合開。 總人數上限:80人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATH5426_ |
課程簡介影片 |
|
核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
課程概述 |
林太家教授推導數學模型的方法與數學分析的技巧,主題如下(上課6週):
1. Introduction to differential equation models
2. Models of molecular dynamic simulations
3. Monte Carlo simulations
4. Energetic variational approaches
5. Conservation laws
6. Drift-diffusion equations
7. Techniques of Fourier analysis
洪子倫教授生理數學建模與模擬,主題如下 (上課3週):
1. Body’s organization. Between-organ interactions. Nervous and hormonal control.
Complexity and chaotic behavior. Time and length scales. Remodeling.
2. Normal and abnormal blood circulation and breathing. Other physiological targets
proposed by attendees.
3. Cell signaling network. Biomathematical modeling. Illustrations according to par-
ticipant research topics.
4. Medical image acquisition and processing. 3D reconstruction. Meshing
5. Biomechanics. Deformable organs. Physiological fluid–solid interaction.
王偉仲教授Mathematical Models in Computational and Data Sciences 主題如下 (上課1週):
1. Introduction to computaitonal and data sciences
2. Equation-based and data-driven models
3. Large-scale singular value decomposition and principal component analysis
4. Examples and perspectives
鄧君豪教授常微、偏微分方程式的數值模擬方法及其應用 (上課6週):
Chun-Hao Teng is charged in concepts and techniques of numerical methods for partial differential equations with applications, which include the following topics:
1. Introduction to numerical partial differential equations (PDEs)
2. Introduction Fourier/polynomial pseudospectral methods for PDEs
3. Multidomain pseudospectral methods for PDEs
4. Pseudospectral schemes for advection-diffusion equations
5. Pseudospectral schemes for PDEs on spherical surfaces
6. Applications of numerical computations in weather predictions
|
課程目標 |
Three abilities will be trained in this course. The first one is to derive mathematical models and use techniques of mathematical analysis to justify models. The second one is to do numerical simulations and the third one is to learn basic knowledge of nanoscience. Students may learn how to do research works by mathematical models in nanoscience. The course would be helpful for students to study problems of different fields of applied mathematics in the future. |
課程要求 |
待補 |
預期每週課後學習時數 |
|
Office Hours |
|
指定閱讀 |
待補 |
參考書目 |
1.Sandip Banerjee, Mathematical Modeling: Models, Analysis and Application, 2014
2. Stein & Shakarchi: I Fourier Analysis: An Introduction
3. Spectral methods in MATLAB, Lloyd N. Trefethen, SIAM, 2000
4. Spectral Methods for Time-Dependent Problems, Jan Hesthaven, Sigal Gottlieb, and David Gottlieb, Cambridge University Press 2007. |
評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
書面報告(ppt) |
100% |
|
|
週次 |
日期 |
單元主題 |
第1週 |
2/24 |
林太家 |
第2週 |
3/03 |
林太家 |
第3週 |
3/10 |
洪子倫 (Marc) |
第4週 |
3/17 |
洪子倫 (Marc) |
第5週 |
3/24 |
洪子倫 (Marc) |
第6週 |
3/31 |
林太家 |
第7週 |
4/07 |
自主學習(氣象局參訪) |
第8週 |
4/14 |
林太家 |
第9週 |
4/21 |
林太家 (Mori) |
第10週 |
4/28 |
林太家 |
第11週 |
5/05 |
王偉仲 |
第12週 |
5/12 |
鄧君豪 |
第13週 |
5/19 |
鄧君豪 |
第14週 |
5/26 |
鄧君豪 |
第15週 |
6/02 |
鄧君豪 |
第16週 |
6/09 |
鄧君豪 |
第17週 |
6/16 |
鄧君豪,氣象建模專題 |
|